Can Bayesian inference be combined with knowledge-based systems?
Yes, it is possible to combine probabilistic / bayesian reasoning and a traditional "knowledgebase".  And some work along those lines has been done.  See, for example, ProbLog ("Probabilistic Prolog") which combines logic programming and probabilistic elements.  See:  

https://dtai.cs.kuleuven.be/problog/tutorial/mpe/01_bn.html

Another project to look at is Pr-OWL
 ("Probabilistic OWL") which adds Bayesian reasoning to the Semantic Web stack.

Of course neither of these deals specifically with QA systems, but both represent some work on at least the foundational aspect of combining traditional logic and/or ontologies, with probabilistic approaches.  Building a QA system on top of that is an exercise for the reader...